Linear and Nonlinear Non-minimal State Space Control System Design

This tutorial chapter uses case studies based on recent engineering applications, to re-examine the non-minimal, state variable feedback approach to control system design. We show how the non-minimal state space (NMSS) representation seems to be the natural description of a discrete-time Transfer Function, since its dimension is dictated by the complete structure of the model. This is in contrast to minimal state space descriptions, which only account for the order of the denominator and whose state variables, therefore, usually represent combinations of input and output signals. The resulting control algorithm can be interpreted as a logical extension of the conventional Proportional-Integral (PI) controller, facilitating its straightforward implementation using a standard hardware-software arrangement. Finally, the basic NMSS approach is readily extended into multivariable, model-predictive and nonlinear control systems, hence the chapter briefly discusses these areas and gives pointers to the latest research results.

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